Trigonometric Fmn-transform of multi-variable functions and its application to the partial differential equations and image processing

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302HZG" target="_blank" >RIV/61988987:17610/22:A2302HZG - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00500-022-07481-2" target="_blank" >https://link.springer.com/article/10.1007/s00500-022-07481-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-022-07481-2" target="_blank" >10.1007/s00500-022-07481-2</a>

Result language
angličtina
Original language name
Trigonometric Fmn-transform of multi-variable functions and its application to the partial differential equations and image processing
Original language description
In this study, we focus on the extention of the trigonometric $F$-transform for functions in one variable to: (i) a larger domain; (ii) a higher degree of the $F^m$-transform, and (iii) many-variable functions to improve its approximation properties over the entire domain and especially at its boundaries. In addition, the properties of approximation and convergence of direct and inverse extended and multidimensional trigonometric $F^{m}$-transforms are discussed. Then direct formulas for partial derivatives of functions of several variables are obtained in terms of trigonometric $F^{m}$-transforms, which are used to solve the Cauchy problem for the transport equation. A new image compression method is proposed and compared with well-established compression methods such as JPEG, JPEG 2000 and their less complex variations JPEG(APDCBT), JPEG(APUBT3), APUBT3-NUP, JPEG-FT. We have shown that this $^tbar{F}^ {11 }$-transform image compression method has high accuracy and reasonably low (irredicible) complexity.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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